Arectangle is a four sided flat shape where every interior is a right angle. therefore, opposite sides are parallel and consecutive sides are perpendicular. rae is drawing rectangle pqrs on a coordinate plane. the rectangle has cord images p(-1,2), q(2,4), r(x, y), and s(3,-4).

coordinates of R(x,y) is R(6,-2).

Step-by-step explanation:

We have given the coordinates of rectangle PQRS as: P(-1,2), Q(2,4), R(x,y), and S(3,-4).

We know the slope formula:

Slope =    

Now, by applying slope formula

Slope of PQ =    

                    =

Slope of RS =    

Slope of QR =  

 We know that, slopes of PQ and RS are equal because these are parallel to each other.

Slope of PQ = Slope of RS

=      

2(3-x) = 3(-4-y)

6-2x = -12-3y

2x-3y = 18...........equation(1)

Slopes of perpendicular lines are negative reciprocal. Therefore,  

Slope of PQ =

=

=

On cross multiplication,

2(y-4) = 3(-x+2)

2y-8 = -3x+6

3x+2y = 14.............equation(2)

Now, multiplying equation(1) by 2 and equation(2) by 3 and then equations are adding..

So,   4x-6y=36

       9x+6y=42

________________

13x=78

x=6

Putting the value of x in equation(2)

18+2y=14

2y=-4

y=-2

So, coordinates of R(x,y) is R(6,-2).

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step-by-step explanation:

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